International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.2, p. 733

Table 3.2.1.5 

Th. Hahna and H. Klappera

Table 3.2.1.5| top | pdf |
Classes of general point groups in two dimensions (N = integer [\geq] 0)

General Hermann–Mauguin symbolOrder of groupGeneral edge formGeneral point formCrystallographic groups
4N-gonal system (n-fold rotation point with [n = 4N])
n n Regular n-gon Regular n-gon 4
nmm 2n Semiregular di-n-gon Truncated n-gon 4mm
[(4N + 2)]-gonal system (n-fold or [{1 \over 2}n]-fold rotation point with [n = 4N + 2])
[{1 \over 2}n] [{1 \over 2}n] Regular [{1 \over 2}n]-gon Regular [{1 \over 2}n]-gon 1, 3
[{1 \over 2}nm] n Semiregular di-[{1 \over 2}n]-gon Truncated [{1 \over 2}n]-gon m, 3m
n n Regular n-gon Regular n-gon 2, 6
nmm 2n Semiregular di-n-gon Truncated n-gon 2mm, 6mm
Circular system
Rotating circle Rotating circle
m Stationary circle Stationary circle
A rotating circle has no mirror lines; there exist two enantiomorphic circles with opposite senses of rotation. A stationary circle has infinitely many mirror lines through its centre.